General Hilbert stacks and Quot schemes

TL;DR

This paper proves the algebraicity of various moduli stacks, including Hilbert, Quot, and coherent sheaves, on algebraic stacks with (quasi-)finite diagonals, extending previous finiteness assumptions.

Contribution

It establishes the algebraicity of these stacks on a broader class of algebraic stacks without finiteness constraints.

Findings

Proves algebraicity of Hilbert functor and stack on algebraic stacks

Establishes algebraicity of Quot functor and stack of coherent sheaves

Provides results for Hom stacks and Weil restrictions

Abstract

We prove the algebraicity of the Hilbert functor, the Hilbert stack, the Quot functor and the stack of coherent sheaves on an algebraic stack X with (quasi-)finite diagonal without any finiteness assumptions on X. We also give similar results for Hom stacks and Weil restrictions.